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El. knyga: Fourier Analysis

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(University of Paris XI, France),
  • Formatas: EPUB+DRM
  • Išleidimo metai: 18-Jan-2017
  • Leidėjas: ISTE Ltd and John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119372233
Kitos knygos pagal šią temą:
Fourier AnalysisDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 18-Jan-2017
  • Leidėjas: ISTE Ltd and John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119372233
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This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is presented followed by a series of corrected exercises. After resolution of these exercises, the reader can pretend to know those principles that are the basis of this theme. "We do not learn anything by word, but by example."
Chapter 1 Fourier Series 1(38)
1.1 Theoretical background
1(8)
1.1.1 Orthogonal functions
1(2)
1.1.2 Fourier Series
3(2)
1.1.3 Periodic functions
5(1)
1.1.4 Properties of Fourier series
6(2)
1.1.5 Discrete spectra. Power distribution
8(1)
1.2 Exercises
9(8)
1.2.1 Exercise 1.1 Examples of decomposition calculations
10(1)
1.2.2 Exercise 1.2
11(1)
1.2.3 Exercise 1.3
12(1)
1.2.4 Exercise 1.4
12(1)
1.2.5 Exercise 1.5
12(1)
1.2.6 Exercise 1.6 Decomposing rectangular functions
13(1)
1.2.7 Exercise 1.7 Translation and composition of functions
14(1)
1.2.8 Exercise 1.8 Time derivation of a function
15(1)
1.2.9 Exercise 1.9 Time integration of functions
15(1)
1.2.10 Exercise 1.10
15(1)
1.2.11 Exercise 1.11 Applications in electronic circuits
16(1)
1.3 Solutions to the exercises
17(22)
1.3.1 Exercise 1.1 Examples of decomposition calculations
17(8)
1.3.2 Exercise 1.2
25(1)
1.3.3 Exercise 1.3
26(1)
1.3.4 Exercise 1.4
26(1)
1.3.5 Exercise 1.5
27(1)
1.3.6 Exercise 1.6
27(2)
1.3.7 Exercise 1.7 Translation and composition of functions
29(2)
1.3.8 Exercise 1.8 Time derivation of functions
31(1)
1.3.9 Exercise 1.9 Time integration of functions
32(1)
1.3.10 Exercise 1.10
32(3)
1.3.11 Exercise 1.11
35(4)
Chapter 2 Fourier Transform 39(58)
2.1 Theoretical background
39(17)
2.1.1 Fourier transform
39(3)
2.1.2 Properties of the Fourier transform
42(4)
2.1.3 Singular functions
46(5)
2.1.4 Fourier transform of common functions
51(2)
2.1.5 Calculating Fourier transforms using the Dirac impulse method
53(1)
2.1.6 Fourier transform of periodic functions
54(1)
2.1.7 Energy density
54(1)
2.1.8 Upper limits to the Fourier transform
55(1)
2.2 Exercises
56(11)
2.2.1 Exercise 2.1
56(1)
2.2.2 Exercise 2.2
57(1)
2.2.3 Exercise 2.3
58(1)
2.2.4 Exercise 2.4
59(1)
2.2.5 Exercise 2.5
59(1)
2.2.6 Exercise 2.6
59(1)
2.2.7 Exercise 2.7
60(1)
2.2.8 Exercise 2.8
60(1)
2.2.9 Exercise 2.9
61(1)
2.2.10 Exercise 2.10
62(1)
2.2.11 Exercise 2.11
62(1)
2.2.12 Exercise 2.12
63(1)
2.2.13 Exercise 2.13
63(1)
2.2.14 Exercise 2.14
64(1)
2.2.15 Exercise 2.15
64(1)
2.2.16 Exercise 2.16
65(1)
2.2.17 Exercise 2.17
66(1)
2.3 Solutions to the exercises
67(30)
2.3.1 Exercise 2.1
67(1)
2.3.2 Exercise 2.2
68(6)
2.3.3 Exercise 2.3
74(1)
2.3.4 Exercise 2.4
74(2)
2.3.5 Exercise 2.5
76(1)
2.3.6 Exercise 2.6
76(1)
2.3.7 Exercise 2.7
77(2)
2.3.8 Exercise 2.8
79(3)
2.3.9 Exercise 2.9
82(3)
2.3.10 Exercise 2.10
85(1)
2.3.11 Exercise 2.11
86(2)
2.3.12 Exercise 2.12
88(3)
2.3.13 Exercise 2.13
91(1)
2.3.14 Exercise 2.14
91(1)
2.3.15 Exercice 2.15
92(2)
2.3.16 Exercise 2.16
94(1)
2.3.17 Exercise 2.17
95(2)
Chapter 3 Laplace Transform 97(46)
3.1 Theoretical background
97(14)
3.1.1 Definition
97(1)
3.1.2 Existence of the Laplace transform
98(1)
3.1.3 Properties of the Laplace transform
98(4)
3.1.4 Final value and initial value theorems
102(1)
3.1.5 Determining reverse transforms
102(3)
3.1.6 Approximation methods
105(2)
3.1.7 Laplace transform and differential equations
107(1)
3.1.8 Table of common Laplace transforms
108(2)
3.1.9 Transient state and steady state
110(1)
3.2 Exercise instruction
111(5)
3.2.1 Exercise 3.1
111(1)
3.2.2 Exercise 3.2
111(1)
3.2.3 Exercise 3.3
112(1)
3.2.4 Exercise 3.4
112(1)
3.2.5 Exercise 3.5
112(1)
3.2.6 Exercise 3.6
113(1)
3.2.7 Exercise 3.7
113(2)
3.2.8 Exercise 3.8
115(1)
3.2.9 Exercise 3.9
115(1)
3.2.10 Exercise 3.10
115(1)
3.3 Solutions to the exercises
116(27)
3.3.1 Exercise 3.1
116(1)
3.3.2 Exercise 3.2
117(4)
3.3.3 Exercise 3.3
121(1)
3.3.4 Exercise 3.4
122(8)
3.3.5 Exercise 3.5
130(1)
3.3.6 Exercise 3.6
131(1)
3.3.7 Exercise 3.7
132(4)
3.3.8 Exercise 3.8
136(2)
3.3.9 Exercise 3.9
138(1)
3.3.10 Exercise 3.10
139(4)
Chapter 4 Integrals and Convolution Product 143(26)
4.1 Theoretical background
143(6)
4.1.1 Analyzing linear systems using convolution integrals
143(1)
4.1.2 Convolution properties
144(1)
4.1.3 Graphical interpretation of the convolution product
145(1)
4.1.4 Convolution of a function using a unit impulse
145(2)
4.1.5 Step response from a system
147(1)
4.1.6 Eigenfunction of a convolution operator
148(1)
4.2 Exercises
149(4)
4.2.1 Exercise 4.1
149(1)
4.2.2 Exercise 4.2
150(1)
4.2.3 Exercise 4.3
150(1)
4.2.4 Exercise 4.4
151(1)
4.2.5 Exercise 4.5
151(1)
4.2.6 Exercise 4.6
152(1)
4.3 Solutions to the exercises
153(16)
4.3.1 Exercise 4.1
153(3)
4.3.2 Exercise 4.2
156(4)
4.3.3 Exercise 4.3
160(3)
4.3.4 Exercise 4.4
163(1)
4.3.5 Exercise 4.5
164(1)
4.3.6 Exercise 4.6
165(4)
Chapter 5 Correlation 169(44)
5.1 Theoretical background
169(8)
5.1.1 Comparing signals
169(1)
5.1.2 Correlation function
170(2)
5.1.3 Properties of correlation functions
172(4)
5.1.4 Energy of a signal
176(1)
5.2 Exercises
177(6)
5.2.1 Exercise 5.1
177(1)
5.2.2 Exercise 5.2
178(1)
5.2.3 Exercise 5.3
178(1)
5.2.4 Exercise 5.4
178(1)
5.2.5 Exercise 5.5
179(1)
5.2.6 Exercise 5.6
179(1)
5.2.7 Exercise 5.7
179(1)
5.2.8 Exercise 5.8
180(1)
5.2.9 Exercise 5.9
180(1)
5.2.10 Exercise 5.10
181(1)
5.2.11 Exercise 5.11
181(1)
5.2.12 Exercise 5.12
182(1)
5.2.13 Exercise 5.13
182(1)
5.2.14 Exercise 5.14
183(1)
5.3 Solutions to the exercises
183(30)
5.3.1 Exercise 5.1
183(5)
5.3.2 Exercise 5.2
188(3)
5.3.3 Exercise 5.3
191(1)
5.3.4 Exercise 5.4
192(1)
5.3.5 Exercise 5.5
193(3)
5.3.6 Exercise 5.6
196(1)
5.3.7 Exercise 5.7
197(4)
5.3.8 Exercise 5.8
201(3)
5.3.9 Exercise 5.9
204(1)
5.3.10 Exercise 5.10
205(1)
5.3.11 Exercise 5.11
206(1)
5.3.12 Exercise 5.12
207(1)
5.3.13 Exercise 5.13
208(1)
5.3.14 Exercise 5.14
209(4)
Chapter 6 Signal Sampling 213(32)
6.1 Theoretical background
213(12)
6.1.1 Sampling principle
213(1)
6.1.2 Ideal sampling
214(4)
6.1.3 Finite width sampling
218(3)
6.1.4 Sample and hold (S/H) sampling
221(4)
6.2 Exercises
225(4)
6.2.1 Exercise 6.1
225(1)
6.2.2 Exercise 6.2
225(1)
6.2.3 Exercise 6.3
226(1)
6.2.4 Exercise 6.4
226(1)
6.2.5 Exercise 6.5
226(1)
6.2.6 Exercise 5.6
227(1)
6.2.7 Exercise 6.7
227(1)
6.2.8 Exercise 6.8
228(1)
6.3 Solutions to the exercises
229(16)
6.3.1 Exercise 6.1
229(1)
6.3.2 Exercise 6.2
229(4)
6.3.3 Exercise 6.3
233(2)
6.3.4 Exercise 6.4
235(1)
6.3.5 Exercise 6.5
236(2)
6.3.6 Exercise 6.6
238(2)
6.3.7 Exercise 6.7
240(2)
6.3.8 Exercise 6.8
242(3)
Bibliography 245(2)
Index 247
JL Gautier was a university professor at ENSEA. He retired in 2014. He taught the design of microwave circuits and architecture segments RF digital communications systems. His research activities have focused on the design of integrated monolithic microwave circuits. He is the author of over 100 publications and papers in journals and international conferences.

R Ceschi is the General Director of Esigetel and the Deputy Director General of Efrei Parsi-south group. He teaches theory and signal optimization in engineering schools and abroad. Associate Professsor at the "Cape Peninsula University of Technology" at the "Shanghai Normal University" Visiting Professor at the "Beijing Institute of Technology" and at the "Beijing Institute of Petrochemical Technology"
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